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quest_marsman
 Senior Boarder
Posts: 72 
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What is the next number in this series? 11 12 1121 111221 ?
If you could explain why also, it would be appreciated. I have tried converting to binary (1=0 and 2=1) and grouping it into pairs, but I still can't figure it out.
Thank you,
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bhunders
Senior Boarder
Posts: 67
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Look at the first row. what is it? It is a single '1', ie one '1'.
the second row is just describing the first row: 11, read as 'one 1'.
The second row is two ones. so the third row describes it as 21, read as 'two 1s'.
the third row is a 2 and a 1. ie one 2, one 1. 1211; which is the 4th row.
the fourth row is a 1, a 2, and two 1s. 111221
and so on.
So the next in the sequence is: three 1s, two 2s, one 1. ie 312211
It's fairly easy to see that you can never get a digit larger than 3 in this way.
HTH
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